Rational combinations of Betti diagrams of complete intersections
نویسندگان
چکیده
منابع مشابه
Non-simplicial Decompositions of Betti Diagrams of Complete Intersections
We investigate decompositions of Betti diagrams over a polynomial ring within the framework of Boij–Söderberg theory. That is, given a Betti diagram, we decompose it into pure diagrams. Relaxing the requirement that the degree sequences in such pure diagrams be totally ordered, we are able to define a multiplication law for Betti diagrams that respects the decomposition and allows us to write a...
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Abstract. Let I = (F1, . . . , Fr) be a homogeneous ideal of the ring R = k[x0, . . . , xn] generated by a regular sequence of type (d1, . . . , dr). We give an elementary proof for an explicit description of the graded Betti numbers of Is for any s ≥ 1. These numbers depend only upon the type and s. We then use this description to: (1) write HR/Is , the Hilbert function of R/Is, in terms of HR...
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In this dissertation, we are concerned with decompositions of Betti diagrams over standard graded rings and the information about that ring and its modules that can be recovered from these decompositions. In Chapter 2, we study the structure of modules over short Gorenstein graded rings and determine a necessary condition for a matrix of nonnegative integers to be the Betti diagram of such a mo...
متن کاملThe Semigroup of Betti Diagrams
The recent proof of the Boij-Söderberg conjectures reveals new structure about Betti diagrams of modules, giving a complete description of the cone of Betti diagrams. We begin to expand on this new structure by investigating the semigroup of Betti diagrams. We prove that this semigroup is finitely generated, and we answer several other fundamental questions about this semigroup.
متن کاملGraded Betti Numbers of Cohen-macaulay Modules and the Multiplicity Conjecture
We give conjectures on the possible graded Betti numbers of Cohen-Macaulay modules up to multiplication by positive rational numbers. The idea is that the Betti diagrams should be non-negative linear combinations of pure diagrams. The conjectures are verified in the cases where the structure of resolutions are known, i.e., for modules of codimension two, for Gorenstein algebras of codimension t...
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ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2018
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s0219498818500792